The dependence of the vorticity amplitude on the collision energy and centrality has been studied in [1]} for the initial state of QGP and further simulated in [2]} with a multi-phase transport model(AMPT) for the whole period of QGP evolution. As the qualitative predictions is quite reasonable, ones believe that the traditional understanding on the vorticity should not be completely wrong. Thus from the aspects of kinetic theory, quantum Wigner functions and hydrodynamics, various attempts[3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]} have been made to mend the usual theory which is basing on the straightforward scenario of the parton collisions, such as different vorticity definitions by considering the thermal environment[10]}, [11]} and novel vacuum structures by the strongly rotating system[12]}. In most of these works, quraks, which serve as the visible spin-carries of the final-state hadrons, have attracted almost all the interests[13]}, [14]}. The gluons, which carrying double spins and thus suffered double polarization effects, are neglected because of the technical problems in most cases. As it is closely related with the quantum chromodynamics(QCD)'s fundamental problem, in this work we will only take our first step towards the gluon's part, namely to study the vector field in the present of a background rotation field.
